Just like to add that I asked TP this very question at a book signing. The answers given are very much in line with what he said.
– Loop SpaceAug 18 '18 at 22:30

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There was a Donald Duck, many many years ago, with a story about a salesman trying to sell hand-sized Pyramid replica's. One of it's features was indeed sharpening a razor. While I can't find that story (otherwise I'd have made this an answer), I do have this cartoon from a newspaper (Gadsden Times, November 2 1977).
– MastAug 19 '18 at 11:05

1

@Mast The Donald Duck cartoon references the same thing, but certainly isn't the originator of the superstition.
– mattdmAug 19 '18 at 18:16

@mattdm Oh, definitely. But it goes to show how well-known Pyramid Power story was. As support to the other answers. TP wasn't the first or the last to make jokes about it.
– MastAug 19 '18 at 18:19

4 Answers
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In the real world, there is or was a belief, brought on by the Egyptomania of the early 20th century, that pyramids had special powers—including, specifically, the power to sharpen or maintain the sharpness of razor blades.

Pyramid power refers to the belief that the ancient Egyptian pyramids and objects of similar shape can confer a variety of benefits. Among these assumed properties are the ability to preserve foods, sharpen or maintain the sharpness of razor blades, improve health, function "as a thought-form incubator", trigger sexual urges, and cause other effects. Such unverified theories regarding pyramids are collectively known as pyramidology.

It is beneficial to leave a new blade in the pyramid one to two weeks before using it. It is essential to place it there immediately after the first shave, and not the old, dull one. But it is possible to use an old one, if it is properly resharpened. The blade placed using the method above is left unobstructed until the next shave. The west edge should always face west. It improves the sharpening effect.

This is a reference to the popular myth that placing a razor blade inside a pyramid shape somehow confers magical powers on it, keeping it sharp, something that that inspired multiple patents in the 1950s.

Interestingly, this does actually work in the world of the Discworld, but not for the reasons you might think. Pyramids cause a slowing (and in extreme cases reversal) of time.

By the way, contrary to popular opinion pyramids don’t sharpen razor
blades. They just take them back to when they weren’t blunt. It’s
probably because of quantum.

Pyramid power refers to the belief that the ancient Egyptian pyramids and objects of similar shape can confer a variety of benefits.

Among these assumed properties are the ability to preserve foods, sharpen or maintain the sharpness of razor blades, improve health, function "as a thought-form incubator", trigger sexual urges, and cause other effects.

Such unverified theories regarding pyramids are collectively known as pyramidology.

As an additional note: pyramidology often makes a lot of noise about the precise dimensions of the pyramids and how impossibly advanced the measurements are. (In reality, the Egyptians knew what they were doing, and had perfectly serviceable geometry and tools for the task.)
– CadenceAug 18 '18 at 18:04

A parody of the typical numerical pseudo-science tossed about regarding the Great Pyramid and the 'cosmic truths' (such as the distance from the Earth to the Sun) that the Egyptians supposedly incorporated into its measurements.

The remark about sharpening razor blades at the end of the paragraph is similarly a reference to the pseudo-scientific 'fact' that (small models of) pyramids are supposed to have, among many other powers, the ability to sharpen razor blades that are left underneath the pyramids overnight.